Missing pi digits calculation Message #2 Posted by Karl Schneider on 21 Feb 2007, 3:47 a.m., in response to message #1 by Massimo Gnerucci (Italy)
Hi, Massimo 
Quote:
Sorry Karl, shouldn't that be:
HP41: sin (3.141592654 rad) = 4.1 x 10^{10} vs 4.10206761537 x 10^{10} ?
That also is a correct calculation, but my point was to reveal the ensuing digits of pi by calculating a truncated (not rounded) value of pi in radians mode. I've gone through the exercise several times in the Forum, but didn't save a bookmark to those posts:
sin(pi  x) = sin(pi)*cos(x)  cos(pi)*sin(x)
= 0 * cos(x)  (1)*sin(x)
= sin(x)
x represents the truncated digits. For very small x, sin(x) ~= x, so the result produces a limited string of those digits.
The excellent mathematical routines developed for the Saturn microprocessor (debuting with the HP71B) were ported to the Pioneerseries calculators. No other calculator I own matches the quality of the Saturn mathematics, although the TI89 might. It also seems likely that Valentin's vintage Sharp pocket computers could meet or exceed the accuracy.
 KS
